Anistar City (ヒャッコクシティ Hyakkoku City in japanese) is a city in the region of Kalos, that appears in the sixth generation games, Pokémon X and Pokémon Y. This city is located in the eastern part of Kalos. It's the seventh city you visit through the natural order of the game.
This city is noted by its great meteorite that proceeds from space, similar to a great crystal, that decorates the west part of the city and makes the function of a sun clock. For the rest, this city is very modern, and it has the seventh Pokémon Gym in the region.
Below the Gym, there's a house with an old man that lives alone, and will ask you if you have a Pokémon whose level is 5 or under to make him company.
If you leave a Pokémon and return after several days, you'll find the house empty with a Pokéball in the middle, with your Pokémon, and a note. This note explains that the old man has deceased and he's thanking you for leaving the Pokémon with him. After reading the note, you'll get a Comet Shard and your Pokémon back. Your Pokémon won't get any experience points.